Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups
-
Ravi P. Agarwal
agarwal@fit.edu
-
Michael E. Filippakis
mfilip@math.ntua.gr
-
Donal O‘Regan
donal.oregan@nuigalway.ie
-
Nikolaos S. Papageorgiou
npapg@math.ntua.gr
Downloads
Abstract
We consider a semilinear elliptic equation, with a right hand side nonlinearity which may grow linearly. Throughout we assume a double resonance at infinity in the spectral interval [λ1, λ2]. In this paper, we can also have resonance at zero or even double resonance in the order interval [λm, λm+1], m ≥ 2. Using Morse theory and in particular critical groups, we prove two multiplicity theorems.
Keywords
Most read articles by the same author(s)
- Mircea Balaj, Donal O‘Regan, An Intersection Theorem and its Applications , CUBO, A Mathematical Journal: Vol. 10 No. 4 (2008): CUBO, A Mathematical Journal
- Donal O‘Regan, Reza Saadati, â„’ -Random and Fuzzy Normed Spaces and Classical Theory , CUBO, A Mathematical Journal: Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal
- Aris Aghanians, Donal O‘Regan, Kamal Fallahi, Kourosh Nourouzi, Some coupled coincidence point theorems in partially ordered uniform spaces , CUBO, A Mathematical Journal: Vol. 16 No. 2 (2014): CUBO, A Mathematical Journal
- Yuqing Chen, Donal O‘Regan, Ravi P. Agarwal, Degree theory for the sum of VMO maps and maximal monotone maps , CUBO, A Mathematical Journal: Vol. 13 No. 2 (2011): CUBO, A Mathematical Journal
- Chengjun Guo, Donal O‘Regan, Ravi P. Agarwal, Existence of Periodic Solutions for a Class of Second-Order Neutral Differential Equations with Multiple Deviating Arguments , CUBO, A Mathematical Journal: Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal
- Donal O‘Regan, Fixed point theory for compact absorbing contractions in extension type spaces , CUBO, A Mathematical Journal: Vol. 12 No. 2 (2010): CUBO, A Mathematical Journal
- Ravi P. Agarwal, Triple solutions of constant sign for a system of fredholm integral equations , CUBO, A Mathematical Journal: Vol. 6 No. 3 (2004): CUBO, A Mathematical Journal
Similar Articles
- Abolfazl Sadeghi, Ghasem Alizadeh Afrouzi, Maryam Mirzapour, Investigating the existence and multiplicity of solutions to \(\varphi(x)\)-Kirchhoff problem , CUBO, A Mathematical Journal: Vol. 26 No. 3 (2024)
- S.V. Ludkovsky, Wrap groups of fiber bundles and their structure , CUBO, A Mathematical Journal: Vol. 11 No. 1 (2009): CUBO, A Mathematical Journal
- N. Seshagiri Rao, K. Kalyani, Fixed point results of \((\phi,\psi)\)-weak contractions in ordered \(b\)-metric spaces , CUBO, A Mathematical Journal: Vol. 24 No. 2 (2022)
- Hugo Leiva, Jesús Matute, Nelson Merentes, José Sánchez, On a type of Volterra integral equation in the space of continuous functions with bounded variation valued in Banach spaces , CUBO, A Mathematical Journal: Vol. 17 No. 2 (2015): CUBO, A Mathematical Journal
- Hamza El-Houari, Lalla Saádia Chadli, Hicham Moussa, On a class of fractional Γ(.)-Kirchhoff-Schrödinger system type , CUBO, A Mathematical Journal: Vol. 26 No. 1 (2024)
- Binayak S. Choudhury, Nikhilesh Metiya, Sunirmal Kundu, Existence, well-posedness of coupled fixed points and application to nonlinear integral equations , CUBO, A Mathematical Journal: Vol. 23 No. 1 (2021)
- Bapurao C. Dhage, Some Generalizations of Mulit-Valued Version of Schauder‘s Fixed Point Theorem with Applications , CUBO, A Mathematical Journal: Vol. 12 No. 3 (2010): CUBO, A Mathematical Journal
- Martin Moskowitz, Symmetric Spaces of Noncompact type , CUBO, A Mathematical Journal: Vol. 7 No. 2 (2005): CUBO, A Mathematical Journal
- Rafael Galeano, Pedro Ortega, John Cantillo, Stationary Boltzmann equation and the nonlinear alternative of Leray-Schauder type , CUBO, A Mathematical Journal: Vol. 16 No. 1 (2014): CUBO, A Mathematical Journal
- A. Zerki, K. Bachouche, K. Ait-Mahiout, Existence of solutions for higher order \(\phi-\)Laplacian BVPs on the half-line using a one-sided Nagumo condition with nonordered upper and lower solutions , CUBO, A Mathematical Journal: Vol. 25 No. 2 (2023)
1 2 3 4 5 6 7 8 9 10 11 12 > >>
You may also start an advanced similarity search for this article.
Downloads
Download data is not yet available.
Published
2008-10-01
How to Cite
[1]
R. P. Agarwal, M. E. Filippakis, D. O‘Regan, and N. S. Papageorgiou, “Multiple Solutions for Doubly Resonant Elliptic Problems Using Critical Groups”, CUBO, vol. 10, no. 3, pp. 21–41, Oct. 2008.
Issue
Section
Articles
